**Physiology**

30 New Approaches to the Study of Marine Mammals

Wotton, E. 1552. De differentiis animalium libri decem ... cum amplissimus indicibus, in quibus primùm authorum nomina, unde quaequae desumpta sunt, singulis capitibus sunt notata & designata: deinde omnium animalium nomenclaturae,

itémque singulae eorum partes recensentur, tam Graecè, quàm Latinè. Paris.

**Chapter 2** 

© 2012 Keith, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

**A Matrix Model of Fasting Metabolism** 

Northern elephant seals (*Mirounga angustirostris*) undergo regular periods of aphagia during their annual life cycle, as do many other phocids (Le Boeuf and Laws 1994). After nursing for about 30 days, the weaned pup fasts for 6-8 weeks, maintaining a fasting hyperglycemia, hyperlipidemia, hypoketonemia, and hypoinsulinemia (Champagne, *et al.*  2005). In most mammals, fasting is accompanied by hypoglycemia, and thus the fasting hyperglycemia in these animals is paradoxical. Previous studies of glucose metabolism in these animals (Keith and Ortiz 1989) indicate that the hyperglycemia results from both low rates of glucose utilization, due to very low insulin levels (Kirby, *et. al.* 1987), as well as high rates of glucose carbon recycling through both lactate and glycerol. Other studies indicate that fatty acids are the major energy substrate during this time (Castellini, *et. al.* 1987), and that these animals conserve nitrogen by having very low urea turnover and excretion rates (Houser and Costa 2001). Figure 1 shows a 10 compartment conceptual flow diagram of metabolite flux in fasting northern elephant seal pups as simulated in this

Mathematical models of biochemical systems are a prerequisite for a true understanding of the complexity of metabolic and physiologic systems. A model can be defined in both a physical and mathematical sense as a set of equations that describe the behavior of a dynamic system, and the response of the system to a given stimulus (Jeffers 1982). Many types of models exist. The models that most closely approximate reality are often the most complex, and it is often difficult to derive unbiased or valid estimates of model parameters. Matrix models offer a way to sacrifice some of the "reality" to gain the advantages of mathematical deduction and prediction (Jeffers 1978). Matrix models are ideally suited to simulate the results of isotope tracer experiments and linear compartment analysis models

**in Northern Elephant Seal Pups** 

Additional information is available at the end of the chapter

Edward O. Keith

**1. Introduction** 

study.

(Shipley and Clark 1972).

http://dx.doi.org/10.5772/51863
